Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals
, 2010 A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients and scaled 2-norms.
Grcar, Joseph F.
core +1 more source
A matrix approach to determine optimal predictors in a constrained linear mixed model
Open MathematicsFor a general vector of all unknown vectors in a constrained linear mixed model (CLMM), this study compared the dispersion matrices of the best linear unbiased predictors with any symmetric matrix for determining the optimality of predictors among others.
Güler Nesrin, Büyükkaya Melek Eriş
doaj +1 more source
New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model
مجلة بغداد للعلوم, 2020 This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model.
Mustafa Ismaeel Naif Alheety
doaj
High-dimensional stochastic optimization with the generalized Dantzig estimator [PDF]
, 2008 We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with the Huber loss ...
Lounici, Karim
core +2 more sources
2000 Mathematics Subject Classification: Primary 62C99, sec-ondary 62C10, 62C20, 62J05
, 2016 The paper deals with recovering an unknown vector β ∈ R^p based on the observations Y = Xβ + ∈ξ and Z = X + σζ, where X is an unknown n×p-matrix with n ≥ p, ξ ∈ R^p is a standard white Gaussian noise, ζ is a n × p-matrix with i.i.d. standard Gaussian entries, and ∈, σ ∈ R^+ are known noise levels. It is assumed that X has a large condition number and p
Golubev, Yu., Zimolo, Th.
openaire +1 more source
Aligned Rank Statistics for Repeated Measurement Models with Orthonormal Design, Employing a Chernoff-Savage Approach [PDF]
AMS classifications: 62G10, 62G20; 62J05.aligned rank statistics;orthonormal design matrix;repeated measurements;Chernoff-Savage ...
Einmahl, J.H.J. +3 more
core +1 more source
Blackjack in Holland Casino's: Basic, optimal and winning strategies [PDF]
This paper considers the cardgame Blackjack according to the rules of Holland Casino's in the Netherlands. Expected gains of strategies are derived with simulation and also with analytic tools.
Genugten, B.B. van der
core +1 more source
Pattern classification using polynomial and linear regression [PDF]
In this paper we will classify patterns using an algorithm analogous to the k-means algorithm and the regression polynomial of the degree k (for instance, if k=1 we obtain the regression line, and if k=2 we obtain the regression parable), and the ...
Ciuiu, Daniel
core +1 more source
Methodology and convergence rates for functional linear regression
, 2007 In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range
Hall, Peter, Horowitz, Joel L.
core +2 more sources
Pattern classification using principal components regression [PDF]
In this paper we will classify patterns using an algorithm analogous to the k-means algorithm and the principal components regression (PCR). We will also present a financial application in which we apply PCR if the points represent the interests for ...
Ciuiu, Daniel
core +1 more source